Wireless local area network (WLAN) devices may include a Multiple-Input-Multiple-Output (MIMO) transmitter receiver system. A Maximum Likelihood (ML) MIMO receiver may not know the transmitter Error Vector Magnitude (EVM). This may result degradation at the performance of the ML receiver, at least but not limited to, the 3×3 and higher MIMO modulations.
A problem with a MIMO communication may be as follows (the following is a simplified model): a transmitter of the MIMO may transmit a vector x. Each element in the vector is a member of a set of a (linear) digital modulation such as, for example a Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 16-Quadrature amplitude modulation (QAM), 64-QAM or the like.
A receiver of the MIMO is able to receive a set of receive channels y. The transmitted vector x passes through a matrix representing a channel H. The matrix H includes a plurality of rows k and a plurality of columns l. Each element in the row k and the column l represents the channel between the l' th transmit antenna to the k'th receive chain.
At the receiver, Gaussian noise n is added to the received signal. The mathematical model is therefore y=Hx+n. A Maximum Likelihood receiver tries to find a transmitted constellation point to generate the highest likelihood for the receive signal:
      x    ^    =            arg      x        ⁢    min    ⁢          1                                    (                          2              ⁢              π                        )                                k            /            2                          ⁢                  σ          k                      ⁢                  exp        ⁡                  (                                    1                              2                ⁢                                  σ                  2                                                      ⁢                                          (                                  y                  -                  Hx                                )                            H                        ⁢                          (                              y                -                Hx                            )                                )                    .      This is equivalent to {circumflex over (x)}=argxmin∥y−Hx∥.
The model described above ignores the transmitter noise which is mostly generated from phase noise and power amplifier non-linearity. The disregard for the transmitter noise may cause the ML receiver to place the transmitted constellation point on an error constellation point of a constellation diagram.
The received signal is depicted as y=H(x+nT)+nR. The noise at the receiver is colored and the maximum likelihood search is depicted as
      x    ^    =            arg      x        ⁢    min    ⁢          1                                    (                          2              ⁢              π                        )                                k            /            2                          ⁢                                                        R              n                                                        1            /            2                                ⁢                  exp        ⁡                  (                                    -                              1                2                                      ⁢                                          (                                  y                  -                  Hx                                )                            H                        ⁢                                          R                n                                  -                  1                                            ⁡                              (                                  y                  -                  Hx                                )                                              )                    .      Where Rn is the combined noise covariance matrix at the ML receiver (for example Gaussian noise of the transmitter). Rn=σR2I+σT2HHH where, σR2 is the noise variance at each of the receiver chains, as measured at the receiver and σT2 is the transmitter noise variance, as measured at the transmitter antenna ports. While H is estimated during packet preamble analysis at the ML receiver, the ratio between σR2 and σT2 is not known to the ML receiver and may impair the ML receiver performance. Thus, there is a need to mitigate the above described problems.
It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.